Question

Show that a/(b+1) - a/(b+1)^2 can be written as ab/(b+1)^2

Answer 1

Answer:

Proof

Step-by-step explanation:

$\frac{a}{(b + 1)} - \frac{a}{ {(b + 1)}^{2} }$

Multiply the first fraction (the numerator and the denominator) by

$(b + 1)$

In order to get common denominators for both fractions

$\frac{a(b + 1)}{ {(b + 1)}^{2} } - \frac{a}{ {(b + 1)}^{2} }$

Then expand the first fraction's numerator and subtract fractions to get your answer

$\frac{ab + a}{ {(b + 1)}^{2} } - \frac{a}{ {(b + 1)}^{2} } = \frac{ab}{ {(b + 1)}^{2} }$

Answer 2

Step-by-step explanation:

$\dfrac{a}{b+1} - \dfrac{a}{(b+1)^2} =$

$= \dfrac{b + 1}{b + 1} \times \dfrac{a}{b+1} - \dfrac{a}{(b+1)^2}$

$= \dfrac{a(b + 1)}{(b+1)^2} - \dfrac{a}{(b+1)^2}$

$= \dfrac{ab + a}{(b+1)^2} - \dfrac{a}{(b+1)^2}$

$= \dfrac{ab + a - a}{(b+1)^2}$

$= \dfrac{ab}{(b+1)^2}$